Krilov solvability of unbounded inverse linear problems

Simple item page
dc.contributor.authorCaruso, Noe
dc.contributor.authorMichelangeli, Alessandro
dc.date.accessioned2020-01-23T07:37:33Z
dc.date.available2020-01-23T07:37:33Z
dc.date.issued2020-01-23
dc.description21 p.en_US
dc.description.abstractThe abstract issue of ‘Krylov solvability’ is extensively discussed for the inverse problem Af = g where A is a (possibly unbounded) linear operator on an infinite-dimensional Hilbert space, and g is a datum in the range of A. The question consists of whether the solution f can be approximated in the Hilbert norm by finite linear combinations of g, Ag, A2g, . . . , and whether solutions of this sort exist and are unique. After revisiting the known picture when A is bounded, we study the general case of a densely defined and closed A. Intrinsic operator-theoretic mechanisms are identified that guarantee or prevent Krylov solvability, with new features arising due to the unboundedness. Such mechanisms are checked in the self-adjoint case, where Krylov solvability is also proved by conjugate-gradient-based techniquesen_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35341
dc.language.isoenen_US
dc.publisherSISSAen_US
dc.relation.ispartofseriesSISSA;25/2019/MATE
dc.subjectinverse linear problemsen_US
dc.subjectconjugate gradient methodsen_US
dc.subjectunbounded operators on Hilbert spaceen_US
dc.subjectself-adjoint operatorsen_US
dc.subjectKrylov subspacesen_US
dc.subjectKrylov solutionen_US
dc.titleKrilov solvability of unbounded inverse linear problemsen_US
dc.typePreprinten_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
CM-2019_ubddKrylov_SISSApreprint.pdf
Size:
371.05 KB
Format:
Adobe Portable Document Format
Description:
Preprint
Download
Collections
Preprints